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3x(7x+40)=180
We move all terms to the left:
3x(7x+40)-(180)=0
We multiply parentheses
21x^2+120x-180=0
a = 21; b = 120; c = -180;
Δ = b2-4ac
Δ = 1202-4·21·(-180)
Δ = 29520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29520}=\sqrt{144*205}=\sqrt{144}*\sqrt{205}=12\sqrt{205}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-12\sqrt{205}}{2*21}=\frac{-120-12\sqrt{205}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+12\sqrt{205}}{2*21}=\frac{-120+12\sqrt{205}}{42} $
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